Search results for: student modelling

Authors: Ye Wei, Sitalakshmi Venkatraman, Fahri Benli, Fiona Wahr

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The present digital world poses many challenges to various stakeholders in the education sector. In particular, lecturers of higher education (HE) are faced with the problem of ensuring that students are able to achieve the required learning outcomes despite rapid changes taking place worldwide. Different strategies are adopted to retain student engagement and commitment in classrooms to address the differences in learning habits, preferences and styles of the digital generation of students recently. Further, with the onset of coronavirus disease (COVID-19) pandemic, online classroom has become the most suitable alternate mode of teaching environment to cope with lockdown restrictions. These changes have compounded the problems in the learning engagement and short attention span of HE students. New Agile methodologies that have been successfully employed to manage projects in different fields are gaining prominence in the education domain. In this paper, we present the application of Scrum as an agile methodology to enhance student learning and engagement in an online smart classroom environment. We demonstrate the use of our proposed approach using a case study to teach key topics in information technology that require students to gain technical and business-related data analytics skills.

Keywords: Agile methodology, Scrum, online learning, smart classroom environment, student engagement, active learning.

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Authors: L. A. Muhammad, M. S. Argungu

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Educational data mining (EDM) has recorded substantial considerations. Techniques of data mining in one way or the other have been proposed to dig out out-of-sight knowledge in educational data. The result of the study got assists academic institutions in further enhancing their process of learning and methods of passing knowledge to students. Consequently, the performance of students boasts and the educational products are by no doubt enhanced. This study adopted a student performance prediction model premised on techniques of data mining with Students' Essential Features (SEF). SEF are linked to the learner's interactivity with the e-learning management system. The performance of the student's predictive model is assessed by a set of classifiers, viz. Bayes Network, Logistic Regression, and Reduce Error Pruning Tree (REP). Consequently, ensemble methods of Bagging, Boosting, and Random Forest (RF) are applied to improve the performance of these single classifiers. The study reveals that the result shows a robust affinity between learners' behaviors and their academic attainment. Result from the study shows that the REP Tree and its ensemble record the highest accuracy of 83.33% using SEF. Hence, in terms of the Receiver Operating Curve (ROC), boosting method of REP Tree records 0.903, which is the best. This result further demonstrates the dependability of the proposed model.

Keywords: Ensemble, bagging, Random Forest, boosting, data mining, classifiers, machine learning.

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Authors: PeiWen Liao, Tsung Hau Jen

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This study was conducted to explore the effects of two countries model comparison program in Taiwan and Singapore in TIMSS database. The researchers used Multi-Group Hierarchical Linear Modeling techniques to compare the effects of two different country models and we tested our hypotheses on 4,046 Taiwan students and 4,599 Singapore students in 2007 at two levels: the class level and student (individual) level. Design quality is a class level variable. Student level variables are achievement and self-confidence. The results challenge the widely held view that retention has a positive impact on self-confidence. Suggestions for future research are discussed.

Keywords: Teaching approach, self-confidence, achievement, multi-group HLM.

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Authors: Ikmal Hisyam Mohamad Paris, Lilly Suriani Affendey, Norwati Mustapha

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In this paper we compare the accuracy of data mining methods to classifying students in order to predicting student-s class grade. These predictions are more useful for identifying weak students and assisting management to take remedial measures at early stages to produce excellent graduate that will graduate at least with second class upper. Firstly we examine single classifiers accuracy on our data set and choose the best one and then ensembles it with a weak classifier to produce simple voting method. We present results show that combining different classifiers outperformed other single classifiers for predicting student performance.

Keywords: Classification, Data Mining, Prediction, Combination of Multiple Classifiers.

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Authors: Ewa. M. Sztendur, Neil T. Diamond

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Random Forests are a powerful classification technique, consisting of a collection of decision trees. One useful feature of Random Forests is the ability to determine the importance of each variable in predicting the outcome. This is done by permuting each variable and computing the change in prediction accuracy before and after the permutation. This variable importance calculation is similar to a one-factor-at a time experiment and therefore is inefficient. In this paper, we use a regular fractional factorial design to determine which variables to permute. Based on the results of the trials in the experiment, we calculate the individual importance of the variables, with improved precision over the standard method. The method is illustrated with a study of student attrition at Monash University.

Keywords: Random Forests, Variable Importance, Fractional Factorial Designs, Student Attrition.

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Authors: P. Valdiviezo, G. Riofrio, R. Reategui

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This article describes the implementation of an intelligent agent that provides recommendations for educational resources in a virtual learning environment (VLE). It aims to support pending (undeveloped) student learning activities. It begins by analyzing the proposed VLE data model entities in the recommender process. The pending student activities are then identified, which constitutes the input information for the agent. By using the attribute-based recommender technique, the information can be processed and resource recommendations can be obtained. These serve as support for pending activity development in the course. To integrate this technique, we used an ontology. This served as support for the semantic annotation of attributes and recommended files recovery.

Keywords: Learning activities, educational resource, recommender agent, recommendation technique, ontology.

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Authors: Mohammed Salem Alzahrani

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In this paper, student admission process is studied to optimize the assignment of vacant seats with three main objectives. Utilizing all vacant seats, satisfying all programs of study admission requirements and maintaining fairness among all candidates are the three main objectives of the optimization model. Seat Assignment Method (SAM) is used to build the model and solve the optimization problem with help of Northwest Coroner Method and Least Cost Method. A closed formula is derived for applying the priority of assigning seat to candidate based on SAM.

Keywords: Admission Process Model, Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM).

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Authors: M. Safa, S. Samarasinghe

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An artificial neural network (ANN) approach was used to model the energy consumption of wheat production. This study was conducted over 35,300 hectares of irrigated and dry land wheat fields in Canterbury in the 2007-2008 harvest year.1 In this study several direct and indirect factors have been used to create an artificial neural networks model to predict energy use in wheat production. The final model can predict energy consumption by using farm condition (size of wheat area and number paddocks), farmers- social properties (education), and energy inputs (N and P use, fungicide consumption, seed consumption, and irrigation frequency), it can also predict energy use in Canterbury wheat farms with error margin of ±7% (± 1600 MJ/ha).

Keywords: Artificial neural network, Canterbury, energy consumption, modelling, New Zealand, wheat.

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Authors: Suleiman Obeidat, Adnan Bashir, Wisam Abu Jadayil

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The affect of the attendance percentage, the overall GPA and the number of credit hours the student is enrolled in at specific semester on the grade attained in specific course has been studied. This study has been performed on three courses offered in industrial engineering department at the Hashemite University in Jordan. Study has revealed that the grade attained by a student is strongly affected by the attendance percentage and his overall GPA with a value of R2 of 52.5%. Another model that has been investigated is the relation between the semester GPA and the attendance percentage, the number of credit hours enrolled in at specific semester, and the overall GPA. This model gave us a strong relationship between the semester GPA and attendance percentage and the overall GPA with a value of R2 of 76.2%.

Keywords: Attendance in classes, GPA, Industrial Engineering, Grade

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Authors: S. A. Sadegh Zadeh, C. Kambhampati

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Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

Keywords: All-or-none, computational modelling, mathematical model, transmembrane voltage, action potential.

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Authors: Said C. Fares, Mary A. Fares

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It is well documented that introductory computer programming courses are difficult and that failure rates are high. The aim of this project was to reduce the high failure and withdrawal rates in learning to program. This paper presents a number of changes in module organization and instructional delivery system in teaching CS1. Daily out of class help sessions and tutoring services were applied, interactive lectures and laboratories, online resources, and timely feedback were introduced. Five years of data of 563 students in 21 sections was collected and analyzed. The primary results show that the failure and withdrawal rates were cut by more than half. Student surveys indicate a positive evaluation of the modified instructional approach, overall satisfaction with the course and consequently, higher success and retention rates.

Keywords: Failure Rate, Interactive Learning, Student engagement, CS1.

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Authors: A. Rouili

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In the present paper the results of a numerical study are presented, numerical models were developed to simulate the behaviour of vertical massive dikes. The proposed models were developed according to the geometry, boundary conditions, loading conditions and initial conditions of a physical model taken as reference. The results obtained were compared to the experimental data. As far as the overall behaviour, the displacements and the failure mechanisms of the dikes is concerned, the numerical results were in good agreement with the experimental results, which clearly indicates a good quality of numerical modelling. The validated numerical models were used in a parametric study were the displacements and failure mechanisms were fully investigated. Out of the results obtained, some conclusions and recommendations related to the design of massive dikes are proposed.

Keywords: Water conservation, dikes, risk assessment and numerical modelling.

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Authors: Jing Lu, Malcolm Keech, Weiru Chen

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Web usage mining is an interesting application of data mining which provides insight into customer behaviour on the Internet. An important technique to discover user access and navigation trails is based on sequential patterns mining. One of the key challenges for web access patterns mining is tackling the problem of mining richly structured patterns. This paper proposes a novel model called Web Access Patterns Graph (WAP-Graph) to represent all of the access patterns from web mining graphically. WAP-Graph also motivates the search for new structural relation patterns, i.e. Concurrent Access Patterns (CAP), to identify and predict more complex web page requests. Corresponding CAP mining and modelling methods are proposed and shown to be effective in the search for and representation of concurrency between access patterns on the web. From experiments conducted on large-scale synthetic sequence data as well as real web access data, it is demonstrated that CAP mining provides a powerful method for structural knowledge discovery, which can be visualised through the CAP-Graph model.

Keywords: concurrent access patterns (CAP), CAP mining and modelling, CAP-Graph, web access patterns (WAP), WAP-Graph, Web usage mining.

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Authors: Shivakumar Krishnamurti, Ruchi Agarwal

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The study examines the influence of marital status on consumers of products and services using blogs as a source of information. A pre-designed questionnaire was used to collect the primary data from the respondents (experiences). Data were collected from one hundred and eighty seven respondents residing in and around the Emirates of Sharjah and Dubai of the United Arab Emirates. The collected data was analyzed with the help of statistical tools such as averages, percentages, factor analysis, Student’s t-test and Structural Equation Modelling Technique. Objectives of the study are to know the reasons how married and unmarried or single consumers of products and services are motivated to use blogs as a source of information, to know whether the consumers of products and services irrespective of their marital status share their views and experiences with other bloggers and to know the respondents’ future intentions towards blogging. The study revealed the following: Majority of the respondents have the motivation to blog because they are willing to receive comments on what they post about services, convenience of blogs to search for information about services and products, by blogging respondents share information on the symptoms of a disease/ disorder that may be experienced by someone, helps to share information about ready to cook mix products and are keen to spend more time blogging in the future.

Keywords: Blog, consumer, information, marital status.

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Authors: D. Lingam, D. R. Seenivasagam, P. Chand, C. Yee, J. Chief, R. Ananthanarayanan

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In a post-pandemic workspace, identifying the barriers, solutions, and strategies related to telecommuting becomes crucial. Amidst the COVID-19 outbreak in 2020, remote work emerged as a vital business continuity measure. This study investigates telecommuting’s modern work model, exploring benefits and obstacles. Utilizing Interpretive Structural Modelling, it uncovers barriers hindering telecommuting adoption. A validated set of thirteen barriers is examined through departmental surveys, revealing interrelationships. The resulting model highlights interactions and dependencies, forming a foundational framework. By addressing dominant barriers, a domino effect on subservient barriers is demonstrated. This research fosters further exploration, proposing management strategies for successful telecommuting adoption, reshaping the traditional workspace.

Keywords: Barriers, interpretive structural modelling, post-pandemic, telecommuting.

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Authors: Dag A.H. Samuelsen, Olaf H. Graven

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Introducing Electromagnetic Interference and Electromagnetic Compatibility, or “The Art of Black Magic", for engineering students might be a terrifying experience both for students and tutors. Removing the obstacle of large, expensive facilities like a fully fitted EMC laboratory and hours of complex theory, this paper demonstrates a design of a laboratory setup for student exercises, giving students experience in the basics of EMC/EMI problems that may challenge the functionality and stability of embedded system designs. This is done using a simple laboratory installation and basic measurement equipment such as a medium cost digital storage oscilloscope, at the cost of not knowing the exact magnitude of the noise components, but rather if the noise is significant or not, as well as the source of the noise. A group of students have performed a trial exercise with good results and feedback.

Keywords: EMC, EMI, engineering project, student laboratory.

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Authors: D. Triantakonstantis, D. Stathakis

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Urban areas have been expanded throughout the globe. Monitoring and modelling urban growth have become a necessity for a sustainable urban planning and decision making. Urban prediction models are important tools for analyzing the causes and consequences of urban land use dynamics. The objective of this research paper is to analyze and model the urban change, which has been occurred from 1990 to 2000 using CORINE land cover maps. The model was developed using drivers of urban changes (such as road distance, slope, etc.) under an Artificial Neural Network modelling approach. Validation was achieved using a prediction map for 2006 which was compared with a real map of Urban Atlas of 2006. The accuracy produced a Kappa index of agreement of 0,639 and a value of Cramer's V of 0,648. These encouraging results indicate the importance of the developed urban growth prediction model which using a set of available common biophysical drivers could serve as a management tool for the assessment of urban change.

Keywords: Artificial Neural Networks, CORINE, Urban Atlas, Urban Growth Prediction.

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Authors: José L. Jiménez

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The use of technology in the classroom is an issue that is constantly evolving. Digital age students learn differently than their teachers did, so now the teacher should be constantly evolving their methods and teaching techniques to be more in touch with the student. In this paper a case study presents how were used some of these technologies by accompanying a classroom course, this in order to provide students with a different and innovative experience as their teacher usually presented the activities to develop. As students worked in the various activities, they increased their digital skills by employing unknown tools that helped them in their professional training. The twenty-first century teacher should consider the use of Information and Communication Technologies in the classroom thinking in skills that students of the digital age should possess. It also takes a brief look at the history of distance education and it is also highlighted the importance of integrating technology as part of the student's training.

Keywords: Digital tools, on-line learning, social networks, technology.

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Authors: Amirhossein Karamoozian, Desheng Wu, Behzad Abbasnejad

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Building information modelling (BIM) is a new technology to enhance the efficiency of project management in the construction industry. In addition to the potential benefits of this useful technology, there are various risks and obstacles to applying it in construction projects. In this study, a decision making approach is presented for risk assessment in BIM adoption in construction projects. Various risk factors of exerting BIM during different phases of the project lifecycle are identified with the help of Delphi method, experts’ opinions and related literature. Afterward, Shannon’s entropy and Fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Situation) are applied to derive priorities of the identified risk factors. Results indicated that lack of knowledge between professional engineers about workflows in BIM and conflict of opinions between different stakeholders are the risk factors with the highest priority.

Keywords: Risk, BIM, Shannon’s entropy, Fuzzy TOPSIS, construction projects.

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Authors: Proud Arunrangsiwed

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This study analyzes the crisis management and image repair strategies during the crisis of Mahidol Wittayanusorn School (MWIT) library burning. The library of this school was burned by a 16-year-old-male student on June 6th, 2010. This student blamed the school that the lesson was difficult, and other students were selfish. Although no one was in the building during the fire, it had caused damage to the building, books and electronic supplies around 130 million bahts (4.4 million USD). This event aroused many discourses arguing about the education system and morality. The strategies which were used during crisis were denial, shift the blame, bolstering, minimization, and uncertainty reduction. The results of using these strategies appeared after the crisis. That was the numbers of new students, who registered for the examination to get into this school in the later years, have remained the same.

Keywords: School, crisis management, violence, image repair strategies, uncertainty, burn.

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Authors: Kafuko M. Maria, Namisango Fatuma, Byomire Gorretti

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Mobile learning (m-learning) is steadily growing and has undoubtedly derived benefits to learners and tutors in different learning environments. This paper investigates the variation in benefits derived from enhanced classroom learning through use of m-learning platforms in the context of a developing country owing to the fact that it is still in its initial stages. The study focused on how basic technology-enhanced pedagogic innovation like cell phone-based learning is enhancing classroom learning from the learners’ perspective. The paper explicitly indicates the opportunities presented by enhanced learning to a conventional learning environment like a physical classroom. The findings were obtained through a survey of two universities in Uganda in which data was quantitatively collected, analyzed and presented in a three banded diagram depicting the variation in the obtainable benefits. Learners indicated that a smartphone is the most commonly used device. Learners also indicate that straight lectures, student to student plus student to lecturer communication, accessing learning material and assignments are core activities. In a TEL environment support by smartphones, learners indicated that they conveniently achieve the prior activities plus discussions and group work. Learners seemed not attracted to the possibility of using TEL environment to take lectures, as well as make class presentations. The less attractiveness of these two factors may be due to the teacher centered approach commonly applied in the country’s education system.

Keywords: Technology enhanced learning, mobile learning classroom learning, perceived benefits.

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Authors: Mounir Sayadi, Farhat Fnaiech

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In the framework of adaptive parametric modelling of images, we propose in this paper a new technique based on the Chandrasekhar fast adaptive filter for texture characterization. An Auto-Regressive (AR) linear model of texture is obtained by scanning the image row by row and modelling this data with an adaptive Chandrasekhar linear filter. The characterization efficiency of the obtained model is compared with the model adapted with the Least Mean Square (LMS) 2-D adaptive algorithm and with the cooccurrence method features. The comparison criteria is based on the computation of a characterization degree using the ratio of "betweenclass" variances with respect to "within-class" variances of the estimated coefficients. Extensive experiments show that the coefficients estimated by the use of Chandrasekhar adaptive filter give better results in texture discrimination than those estimated by other algorithms, even in a noisy context.

Keywords: Texture analysis, statistical features, adaptive filters, Chandrasekhar algorithm.

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Authors: A. Khafaji, R. Saadane, J. El Abbadi, M. Belkasmi

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The main objectif of this paper is to present a tool that we have developed subject to characterize and modelling indoor radio channel propagation at millimetric wave. The tool is based on the ray tracing technique (RTT). As, in realistic environment we cannot neglect the significant impact of Human Body Shadowing and other objects in motion on indoor 60 GHz propagation channel. Hence, our proposed model allows a simulation of propagation in a dynamic indoor environment. First, we describe a model of human body. Second, RTT with this model is used to simulate the propagation of millimeter waves in the presence of persons in motion. Results of the simulation show that this tool gives results in agreement with those reported in the literature. Specially, the effects of people motion on temporal channel properties.

Keywords: Simulation. 60 GHz band, Ray Tracing Technique, Indoor channel, Propagation, Human Body Model, Level crossing rate,

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Authors: Abdulrahman A. Alghamdi, Paul M. Mummery, Mohammad A. Sheikh

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In this paper, 3D image based composite unit cell is constructed from high resolution tomographic images. Through-thickness thermal diffusivity and in-plane Young’s modulus are predicted for the composite unit cell. The accuracy of the image based composite unit cell is tested by comparing its results with the experimental results obtained from laser flash and tensile test. The FE predictions are in close agreement with experimental results. Through-thickness thermal diffusivity and in-plane Young’s modulus of a virgin C/C composite are predicted by replacing the properties of air (porosity) with the properties of carbon matrix. The effect of porosity was found to be more profound on thermal diffusivity than young’s modulus.

Keywords: Porosity, C/C composite, image based FE modelling, CMC.

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Authors: Ž. Nikolić, H. Smoljanović, N. Živaljić

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This paper presents numerical model based on finite-discrete element method for analysis of the structural response of dry stone masonry structures under static and dynamic loads. More precisely, each discrete stone block is discretized by finite elements. Material non-linearity including fracture and fragmentation of discrete elements as well as cyclic behavior during dynamic load are considered through contact elements which are implemented within a finite element mesh. The application of the model was conducted on several examples of these structures. The performed analysis shows high accuracy of the numerical results in comparison with the experimental ones and demonstrates the potential of the finite-discrete element method for modelling of the response of dry stone masonry structures.

Keywords: Finite-discrete element method, dry stone masonry structures, static load, dynamic load.

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Authors: Yaşar Baykul, Musa Gürsel, Hacı Sulak, Erhan Ertekin, Ersen Yazıcı, Osman Dülger, Yasin Aslan, Kağan Büyükkarcı

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The reliability of the tools developed to learn the learning styles is essential to find out students- learning styles trustworthily. For this purpose, the psychometric features of Grasha- Riechman Student Learning Style Inventory developed by Grasha was studied to contribute to this field. The study was carried out on 6th, 7th, and 8th graders of 10 primary education schools in Konya. The inventory was applied twice with an interval of one month, and according to the data of this application, the reliability coefficient numbers of the 6 sub-dimensions pointed in the theory of the inventory was found to be medium. Besides, it was found that the inventory does not have a structure with 6 factors for both Mathematics and English courses as represented in the theory.

Keywords: Learning styles, Grasha-Riechmann, reliability, validity.

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Authors: Norazah Mohd Suki, T Ramayah

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e-Government structures permits the government to operate in a more transparent and accountable manner of which it increases the power of the individual in relation to that of the government. This paper identifies the factors that determine customer-s attitude towards e-Government services using a theoretical model based on the Technology Acceptance Model. Data relating to the constructs were collected from 200 respondents. The research model was tested using Structural Equation Modeling (SEM) techniques via the Analysis of Moment Structure (AMOS 16) computer software. SEM is a comprehensive approach to testing hypotheses about relations among observed and latent variables. The proposed model fits the data well. The results demonstrated that e- Government services acceptance can be explained in terms of compatibility and attitude towards e-Government services. The setup of the e-Government services will be compatible with the way users work and are more likely to adopt e-Government services owing to their familiarity with the Internet for various official, personal, and recreational uses. In addition, managerial implications for government policy makers, government agencies, and system developers are also discussed.

Keywords: E-government, structural equation modelling, attitude, service.

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Authors: M. Capocelli, A. Caputo, M. De Falco, D. Mazzei, V. Piemonte

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This paper presents the experimental results and the related modeling of a thermal energy storage (TES) facility, ideated and realized by ENEA and realizing the thermocline with an innovative geometry. Firstly, the thermal energy exchange model of an equivalent shell & tube heat exchanger is described and tested to reproduce the performance of the spiral exchanger installed in the TES. Through the regression of the experimental data, a first-order thermocline model was also validated to provide an analytical function of the thermocline, useful for the performance evaluation and the comparison with other systems and implementation in simulations of integrated systems (e.g. power plants). The experimental data obtained from the plant start-up and the short-cut modeling of the system can be useful for the process analysis, for the scale-up of the thermal storage system and to investigate the feasibility of its implementation in actual case-studies.

Keywords: Thermocline, modelling, heat exchange, spiral, shell, tube.

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Authors: Amudha Kadirvelu, Sivalal Sadasivan

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While the problem based learning (PBL) approach promotes unsupervised self-directed learning (SDL), many students experience difficulty juggling the role of being an information recipient and information seeker. Logbooks have been used to assess trainee doctors but not in other areas. This study aimed to determine the effectiveness of logbook for assessing SDL during PBL sessions in first year medical students. The log book included a learning checklist and knowledge and skills components. Comparisons with the baseline assessment of student performance in PBL and that at semester end after logbook intervention showed significant improvements in student performance (31.5 ± 8 vs. 17.7 ± 4.4; p<0.001) with a large effect size of 3.93. The learner-s log for PBL has played an important role in enhancing SDL in first year medical students. Learner-s log could be a good self-assessment tool for the undergraduate medical students.

Keywords: Problem based learning, self-directed learning, logbook, self-assessment.

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Authors: Stephen Barnes, Ian Mills, Frances Cleary

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Augmented and Virtual Reality based applications offer many benefits for the heritage and tourism sector. This technology provides a platform to showcase the regions of interest to people without the need for them to be physically present, which has had a positive impact on enticing tourists to visit those locations. However, the technology also provides the opportunity to present historical artefacts in a form that accurately represents their original, intended appearance. Three sites of interest were identified in the Lingaun Valley in South East Ireland wherein virtual representations of site specific artefacts of interest were created via a multidisciplinary team encompassing archaeology, art history, 3D modelling, design and software development. The collated information has been presented to users via an Augmented Reality mobile based application that provides information in an engaging manner that encourages an interest in history as well as visits to the sites in the Lingaun Valley.

Keywords: Augmented Reality, Virtual Heritage, 3D modelling, archaeology, virtual representation.

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